# Assume that the returns of individual securities are generated by the following two factor model

## Question: Assume that the returns of individual securities are generated by the following two factor

Assume that the returns of individual securities are generated by the following two factor model:

R_{it} = E [R_{it}] + βi1F1t+ βi2F2t,

Where R_{it} is return on security i at time t, F1t and F2t are two systematic factors with mean zero. We also assume that F1t and F2t are uncorrelated with each other. We have the following information about three securities:

Security E[R] β1 β2

1 10% 1 2

2 12% 1.5 2

3 8% 0 1

The risk-free rate is 6%.

(a) Consider a portfolio with 25% in security 1 and 75% in security 2. What are the betas of the portfolio with respect to the two factors?

(b) Construct a portfolio of the three securities (with weights summed up equal to one) such that the portfolio’s beta with respect to the first factor is 1 and its beta with respect to the second factor is 0. What is the expected return of this portfolio?

(c) According to the APT, what are the theoretical expected returns of securities land 2? (Hint: Security 3 has zero beta with respect to the first factor and unit beta with respect to the second factor.)

(d) Is security 1 overpriced or underpriced? Describe a possible trading strategy in such detail that an investor could implement it to realize arbitrage profit from them is pricing of security 1.

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